Egypt's opposition plans new protests on Tuesday (local time) against a planned Islamist-backed constitution that looks set to be approved in the second round of a referendum next weekend.

Islamist President Mohamed Mursi obtained a 57 per cent "yes" vote for the constitution in initial voting on Saturday, his party said, less than he had hoped for.

The result is likely to embolden the opposition, which says the law is too Islamist, although the second round is expected to result in another "yes", while underlining the deep divisions that have riven Egypt since Hosni Mubarak's fall.

On Monday, protesters broke out into cheers when the public prosecutor Mursi appointed just last month announced his resignation. They said it was a victory for the independence of the judiciary.

But they are unlikely to win Saturday's referendum second round, to be held in districts seen as even more sympathetic towards Mursi's Muslim Brotherhood, which won elections held after Mubarak was ousted in February 2011.

The opposition National Salvation Front said there were widespread voting violations in the first round of the referendum vote and urged organisers to ensure that the second round was properly supervised.

It has called for protests across Egypt on Tuesday "to stop forgery and bring down the invalid draft constitution" and wants organisers to re-run the first round of voting.

In Cairo, the Front plans to hold demonstrations at Tahrir Square, cradle of the revolution that toppled Mubarak, and outside Mursi's presidential palace, still ringed with tanks after earlier protests.

"Down with the constitution of the Brotherhood," the Front said in a statement. "Down with the constitution of tyranny."

The build-up to the first round saw clashes between supporters and opponents of Mursi in which eight people died. Demonstrations in Cairo have been more peaceful, although rival factions clashed on Friday in Alexandria, Egypt's second biggest city.

On Monday, more than 1300 members of the General Prosecution gathered outside the office of Public Prosecutor Talaat Ibrahim to demand that he leave his post.

Hours later, Ibrahim announced he had resigned and the crowd cheered, "God is Great! Long live justice!" and "Long live the independence of the judiciary!" witnesses said.

Official results of the referendum will come only after the second round, but one newspaper calculated that out of every 100 Egyptians, 18 voted "yes", 13 voted "no" and the rest did not participate, buttressing opposition claims that Mursi had failed to secure real backing.

The closeness of the first-round tally and low turnout give Mursi scant comfort as he seeks to assemble support for difficult economic reforms to reduce the budget deficit.

He will hold a further round of national unity talks with political leaders on Tuesday, but the National Salvation Front is expected to stay away, as it has in the past.

OPPOSITION BOOST

The lack of a clear result in the plebiscite so far has complicated matters for Mursi, strengthening the fractious opposition and casting doubt over the credibility of the constitution, political analysts believe.

"This percentage ... will strengthen the hand of the National Salvation Front and the leaders of this Front have declared they are going to continue this fight to discredit the constitution," said Mustapha Kamal Al-Sayyid, a professor of political science at Cairo University.

Mursi would be likely to become more unpopular with the introduction of planned austerity measures, polarising society further, Sayyid told Reuters.

If the constitution passes next weekend, national elections can take place early next year, something many hope will usher in a much-needed period of stability in Egypt.

To tackle the budget deficit, the government needs to impose tax rises and cut back fuel subsidies. Uncertainty surrounding economic reform plans has already forced the postponement of a $4.8 billion loan from the International Monetary Fund. The Egyptian pound has fallen to eight-year lows against the dollar.

Mursi and his backers say the constitution is vital to moving Egypt's democratic transition forward. Opponents say the document is too Islamist and ignores the rights of women and of minorities, including Christians who make up 10 percent of the population.

Demonstrations erupted when Mursi awarded himself extra powers on November 22 and then fast-tracked the constitution through an assembly dominated by his Islamist allies and boycotted by many liberals.

The referendum is being held over two days because many of the judges needed to oversee polling staged a boycott in protest. In order to pass, the constitution must be approved by more than 50 percent of those casting ballots.